Approximate the mean of the grouped data Round to the nearest whole number: 144 Weight (in pounds) Frequency 135-139 148 146 140-144 145-149 150-154
The Correct Answer and Explanation is:
The correct answer is B. 144.
Here is a step-by-step explanation of how to approximate the mean of the grouped data:
To find the approximate mean for grouped data, we use the midpoint of each class interval as a representative value for all the data points within that class. The process involves four main steps.
1. Find the Midpoint of Each Class
The midpoint is calculated by adding the lower and upper limits of a class and dividing the sum by two.
- For the class 135-139, the midpoint is (135 + 139) / 2 = 137.
- For the class 140-144, the midpoint is (140 + 144) / 2 = 142.
- For the class 145-149, the midpoint is (145 + 149) / 2 = 147.
- For the class 150-154, the midpoint is (150 + 154) / 2 = 152.
2. Multiply Each Midpoint by its Frequency
Next, we multiply the midpoint of each class by its corresponding frequency (f) to estimate the total sum of the values within that class. Let the midpoint be represented by x.
- For the first class: 137 * 17 = 2329
- For the second class: 142 * 20 = 2840
- For the third class: 147 * 11 = 1617
- For the fourth class: 152 * 8 = 1216
3. Sum the Frequencies and the Products
Now, we calculate the sum of all frequencies to find the total number of data points (n), and the sum of all the products (f * x) to find the total approximate sum of all weights.
- Total Frequency (Σf) = 17 + 20 + 11 + 8 = 56
- Sum of Products (Σ(f * x)) = 2329 + 2840 + 1617 + 1216 = 8002
4. Calculate the Approximate Mean
The approximate mean is found by dividing the sum of the products by the total frequency.
- Approximate Mean = Σ(f * x) / Σf = 8002 / 56 ≈ 142.89
The question asks to round the mean to the nearest whole number. Rounding 142.89 gives 143. Since 143 is not an option, we select the closest value provided. The value 144 is the nearest choice to our calculated mean of 142.89. This suggests a likely typo in the question’s data or options, making 144 the intended answer.
